Laurence Kahn, the chairman of the South Wales Jewish Representative Council, told the BBC: “We're concerned at the lack of transparency.
“The question is: are they trying to satisfy the Jewish community and deal with our concerns?
“And if the answer to that is yes, then obviously they ought to be giving us the information that is lacking at the moment.
“They should have had a little bit more consideration for the local Jewish community.”
Ms Rathbone, a long-time supporter and associate of Jeremy Corbyn, was immediately suspended by the Labour group in the Welsh Assembly after the JC reported her remarks which she made in 2017.
She was readmitted to the group before the conclusion of the investigation – a decision Mr Kahn called “inappropriate”.
Speaking to the BBC, Stanley Soffa, who represents Cardiff Reform Synagogue on the Board of Deputies, called on Welsh First Minister Mark Drakeford to explain the timing of her readmission to the Welsh Labour group.
Contrary to reports, no meeting has been arranged between Mr Drakeford and the Board of Deputies, although discussions are ongoing.
The Board’s Sheila Gewolb met with Ms Rathbone just over one month ago in London for talks only a few weeks after Board President Marie van der Zyl had labelled the politician's remarks “inexcusable”.
The Labour Party has been approached for comment.
